For more information about this meeting, contact Becky Halpenny.

Title: | "Modular forms for finite index subgroups of SL(2,Z)" |

Seminar: | Ph.D. Oral Comprehensive Examination |

Speaker: | Will Chen, Adviser: Wen-Ching W. Li, Penn State |

Abstract: |

Since its inception, the theory of modular forms has almost exclusively focused on modular forms for congruence subgroups, for which a beautiful and deep theory has been developed culminating in the celebrated proof of the modularity theorem and FLT. On the other hand, very little is known about the world of modular forms for noncongruence subgroups. A theorem of Belyi implies that every smooth projective curve defined over a number field can be realized as a modular curve, usually noncongruence. Thus, noncongruence modular curves are very general, and one might expect that as a result, relatively little can be said about them. On the other hand, their uniformization by the upper half plane is rather special, and hence one might hope that there maybe be at least certain classes of noncongruence modular curves for which a theory comparable to that of congruence curves may be established.
In my talk, I'll compare the two worlds, highlighting their key differences, as well as some striking similarities. I will conclude the talk by presenting some directions for further investigation. |

### Room Reservation Information

Room Number: | MB113 |

Date: | 04 / 30 / 2013 |

Time: | 10:00am - 12:00pm |